Data-driven multivariate and multiscale methods for brain computer interface

This thesis focuses on the development of data-driven multivariate and multiscale methods for brain computer interface (BCI) systems. The electroencephalogram (EEG), the most convenient means to measure neurophysiological activity due to its noninvasive nature, is mainly considered. The nonlinearity and nonstationarity inherent in EEG and its multichannel recording nature require a new set of data-driven multivariate techniques to estimate more accurately features for enhanced BCI operation. Also, a long term goal is to enable an alternative EEG recording strategy for achieving long-term and portable monitoring. Empirical mode decomposition (EMD) and local mean decomposition (LMD), fully data-driven adaptive tools, are considered to decompose the nonlinear and nonstationary EEG signal into a set of components which are highly localised in time and frequency. It is shown that the complex and multivariate extensions of EMD, which can exploit common oscillatory modes within multivariate (multichannel) data, can be used to accurately estimate and compare the amplitude and phase information among multiple sources, a key for the feature extraction of BCI system. A complex extension of local mean decomposition is also introduced and its operation is illustrated on two channel neuronal spike streams. Common spatial pattern (CSP), a standard feature extraction technique for BCI application, is also extended to complex domain using the augmented complex statistics. Depending on the circularity/noncircularity of a complex signal, one of the complex CSP algorithms can be chosen to produce the best classification performance between two different EEG classes. Using these complex and multivariate algorithms, two cognitive brain studies are investigated for more natural and intuitive design of advanced BCI systems. Firstly, a Yarbus-style auditory selective attention experiment is introduced to measure the user attention to a sound source among a mixture of sound stimuli, which is aimed at improving the usefulness of hearing instruments such as hearing aid. Secondly, emotion experiments elicited by taste and taste recall are examined to determine the pleasure and displeasure of a food for the implementation of affective computing. The separation between two emotional responses is examined using real and complex-valued common spatial pattern methods. Finally, we introduce a novel approach to brain monitoring based on EEG recordings from within the ear canal, embedded on a custom made hearing aid earplug. The new platform promises the possibility of both short- and long-term continuous use for standard brain monitoring and interfacing applications

Seismic characterisation based on time-frequency spectral analysis

We present high-resolution time-frequency spectral analysis schemes to better resolve seismic images for the purpose of seismic and petroleum reservoir characterisation. Seismic characterisation is based on the physical properties of the Earth's subsurface media, and these properties are represented implicitly by seismic attributes. Because seismic traces originally presented in the time domain are non-stationary signals, for which the properties vary with time, we characterise those signals by obtaining seismic attributes which are also varying with time. Among the widely used attributes are spectral attributes calculated through time-frequency decomposition. Time-frequency spectral decomposition methods are employed to capture variations of a signal within the time-frequency domain. These decomposition methods generate a frequency vector at each time sample, referred to as the spectral component. The computed spectral component enables us to explore the additional frequency dimension which exists jointly with the original time dimension enabling localisation and characterisation of patterns within the seismic section. Conventional time-frequency decomposition methods include the continuous wavelet transform and the Wigner-Ville distribution. These methods suffer from challenges that hinder accurate interpretation when used for seismic interpretation. Continuous wavelet transform aims to decompose signals on a basis of elementary signals which have to be localised in time and frequency, but this method suffers from resolution and localisation limitations in the time-frequency spectrum. In addition to smearing, it often emerges from ill-localisation. The Wigner-Ville distribution distributes the energy of the signal over the two variables time and frequency and results in highly localised signal components. Yet, the method suffers from spurious cross-term interference due to its quadratic nature. This interference is misleading when the spectrum is used for interpretation purposes. For the specific application on seismic data the interference obscures geological features and distorts geophysical details. This thesis focuses on developing high fidelity and high-resolution time-frequency spectral decomposition methods as an extension to the existing conventional methods. These methods are then adopted as means to resolve seismic images for petroleum reservoirs. These methods are validated in terms of physics, robustness, and accurate energy localisation, using an extensive set of synthetic and real data sets including both carbonate and clastic reservoir settings. The novel contributions achieved in this thesis include developing time-frequency analysis algorithms for seismic data, allowing improved interpretation and accurate characterisation of petroleum reservoirs. The first algorithm established in this thesis is the Wigner-Ville distribution (WVD) with an additional masking filter. The standard WVD spectrum has high resolution but suffers the cross-term interference caused by multiple components in the signal. To suppress the cross-term interference, I designed a masking filter based on the spectrum of the smoothed-pseudo WVD (SP-WVD). The original SP-WVD incorporates smoothing filters in both time and frequency directions to suppress the cross-term interference, which reduces the resolution of the time-frequency spectrum. In order to overcome this side-effect, I used the SP-WVD spectrum as a reference to design a masking filter, and apply it to the standard WVD spectrum. Therefore, the mask-filtered WVD (MF-WVD) can preserve the high-resolution feature of the standard WVD while suppressing the cross-term interference as effectively as the SP-WVD. The second developed algorithm in this thesis is the synchrosqueezing wavelet transform (SWT) equipped with a directional filter. A transformation algorithm such as the continuous wavelet transform (CWT) might cause smearing in the time-frequency spectrum, i.e. the lack of localisation. The SWT attempts to improve the localisation of the time-frequency spectrum generated by the CWT. The real part of the complex SWT spectrum, after directional filtering, is capable to resolve the stratigraphic boundaries of thin layers within target reservoirs. In terms of seismic characterisation, I tested the high-resolution spectral results on a complex clastic reservoir interbedded with coal seams from the Ordos basin, northern China. I used the spectral results generated using the MF-WVD method to facilitate the interpretation of the sand distribution within the dataset. In another implementation I used the SWT spectral data results and the original seismic data together as the input to a deep convolutional neural network (dCNN), to track the horizons within a 3D volume. Using these application-based procedures, I have effectively extracted the spatial variation and the thickness of thinly layered sandstone in a coal-bearing reservoir. I also test the algorithm on a carbonate reservoir from the Tarim basin, western China. I used the spectrum generated by the synchrosqueezing wavelet transform equipped with directional filtering to characterise faults, karsts, and direct hydrocarbon indicators within the reservoir. Finally, I investigated pore-pressure prediction in carbonate layers. Pore-pressure variation generates subtle changes in the P-wave velocity of carbonate rocks. This suggests that existing empirical relations capable of predicting pore-pressure in clastic rocks are unsuitable for the prediction in carbonate rocks. I implemented the prediction based on the P-wave velocity and the wavelet transform multi-resolution analysis (WT-MRA). The WT-MRA method can unfold information within the frequency domain via decomposing the P-wave velocity. This enables us to extract and amplify hidden information embedded in the signal. Using Biot's theory, WT-MRA decomposition results can be divided into contributions from the pore-fluid and the rock framework. Therefore, I proposed a pore-pressure prediction model which is based on the pore-fluid contribution, calculated through WT-MRA, to the P-wave velocity.Open Acces

Linear and synchrosqueezed time–frequency representations revisited:overview, standards of use, resolution, reconstruction, concentration, and algorithms

Time–frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed versions (SWFT, SWT), provide powerful analysis tools. Here we present a thorough review of these TFRs, summarizing all practically relevant aspects of their use, reconsidering some conventions and introducing new concepts and procedures to advance their applicability and value. Furthermore, a detailed numerical and theoretical study of three specific questions is provided, relevant to the application of these methods, namely: the effects of the window/wavelet parameters on the resultant TFR; the relative performance of different approaches for estimating parameters of the components present in the signal from its TFR; and the advantages/drawbacks of synchrosqueezing. In particular, we show that the higher concentration of the synchrosqueezed transforms does not seem to imply better resolution properties, so that the SWFT and SWT do not appear to provide any significant advantages over the original WFT and WT apart from a more visually appealing pictures. The algorithms and Matlab codes used in this work, e.g. those for calculating (S)WFT and (S)WT, are freely available for download

Multivariate time-frequency analysis

Recent advances in time-frequency theory have led to the development of high resolution time-frequency algorithms, such as the empirical mode decomposition (EMD) and the synchrosqueezing transform (SST). These algorithms provide enhanced localization in representing time varying oscillatory components over conventional linear and quadratic time-frequency algorithms. However, with the emergence of low cost multichannel sensor technology, multivariate extensions of time-frequency algorithms are needed in order to exploit the inter-channel dependencies that may arise for multivariate data. Applications of this framework range from filtering to the analysis of oscillatory components. To this end, this thesis first seeks to introduce a multivariate extension of the synchrosqueezing transform, so as to identify a set of oscillations common to the multivariate data. Furthermore, a new framework for multivariate time-frequency representations is developed using the proposed multivariate extension of the SST. The performance of the proposed algorithms are demonstrated on a wide variety of both simulated and real world data sets, such as in phase synchrony spectrograms and multivariate signal denoising. Finally, multivariate extensions of the EMD have been developed that capture the inter-channel dependencies in multivariate data. This is achieved by processing such data directly in higher dimensional spaces where they reside, and by accounting for the power imbalance across multivariate data channels that are recorded from real world sensors, thereby preserving the multivariate structure of the data. These optimized performance of such data driven algorithms when processing multivariate data with power imbalances and inter-channel correlations, and is demonstrated on the real world examples of Doppler radar processing.Open Acces

Analysis and decomposition of frequency modulated multicomponent signals

Frequency modulated (FM) signals are studied in many research fields, including seismology, astrophysics, biology, acoustics, animal echolocation, radar and sonar. They are referred as multicomponent signals (MCS), as they are generally composed of multiple waveforms, with specific time-dependent frequencies, known as instantaneous frequencies (IFs). Many applications require the extraction of signal characteristics (i.e. amplitudes and IFs). that is why MCS decomposition is an important topic in signal processing. It consists of the recovery of each individual mode and it is often performed by IFs separation. The task becomes very challenging if the signal modes overlap in the TF domain, i.e. they interfere with each other, at the so-called non-separability region. For this reason, a general solution to MCS decomposition is not available yet. As a matter of fact, the existing methods addressing overlapping modes share the same limitations: they are parametric, therefore they adapt only to the assumed signal class, or they rely on signal-dependent and parametric TF representations; otherwise, they are interpolation techniques, i.e. they almost ignore the information corrupted by interference and they recover IF curve by some fitting procedures, resulting in high computational cost and bad performances against noise. This thesis aims at overcoming these drawbacks, providing efficient tools for dealing with MCS with interfering modes. An extended state-of-the-art revision is provided, as well as the mathematical tools and the main definitions needed to introduce the topic. Then, the problem is addressed following two main strategies: the former is an iterative approach that aims at enhancing MCS' resolution in the TF domain; the latter is a transform-based approach, that combines TF analysis and Radon Transform for separating individual modes. As main advantage, the methods derived from both the iterative and the transform-based approaches are non-parametric, as they do not require specific assumptions on the signal class. As confirmed by the experimental results and the comparative studies, the proposed approach contributes to the current state of the-art improvement